The present invention is directed to a method for fast decoding of output signals of sigma delta modulators, i.e. for fast generation of a high-resolution digital code with normal sampling frequency from a temporally highly over-sampled code having far lower resolution, whereby both codes approximate a temporally sampled, analog signal in digital form. The input signal of a sigma delta modulator is utilized for analog-to-digital conversion.
Sigma delta modulators (J. C. Candy et al. (Eds.), Oversampling Sigma Delta Converters. New York: IEEE Press, 1991.) are simple, highly non-linear circuits that can be used for analog-to-digital conversion, for example for voice or audio signals in audio technology, but which can also be used in many other areas of information and communication technology such as, for example, in communications technology. They can be very cost-beneficially manufactured with the simple processes standard for digital circuits and can be integrated on a chip together with digital circuits. High-precision and, thus, expensive components are not required for building them. The required high resolution is instead achieved by an increased clock rate in combination with a closed, self-correcting, feedback signal loop according to the principle of difference pulse code modulation (DPCM).
An analog input signal that is temporally sampled far above the Nyquist frequency is converted by a sigma delta modulator into an extremely roughly quantized, and extremely over-sampled output signal. The quantization is normally single-stage, so that the output signal of the modulator is binary in the typical case. This binary, extremely over-sampled signal must now be converted into a high-resolution signal, i.e. into a digital signal having a greater word width of, for example, 16 bits which, however, dare have only a substantially lower sampling frequency instead. This procedure is also referred to as decoding.
The conventional methods for decoding the output signals of sigma delta modulators that are based on linear filtering (A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, Prentice Hall: Englewood Cliffs, N.J., 1989) are not able to extract all of the relevant information from the output signal. These methods only use the limitation of the spectrum of the analog input signal to a specific band, but make no use of the specific type of bit-by-bit, sequential generation of the binary data stream by the modulator, i.e. of the relationship between the input signal and the output signal established by the architecture of the modulator. For this reason, the results of these conventional methods based on linear filtering involve errors in the form of too poor a signal-to-noise ratio that can frequently not be tolerated.
Hein and Zakhor describe a non-linear method for decoding sigma delta modulators (S. Hein and A. Zakhor, Sigma Delta Modulators: Nonlinear Decoding Algorithms and Stability Analysis, Kluwer Academic Publishers, 1993, S. Hein and A. Zakhor. Optimal Decoding for Data Acquisition Applications of Sigma Delta Modulators, U.S. Pat. No. 5,164,727, Nov. 17, 1992.) with which a substantially improved signal-to-noise ratio can be achieved. This method is based on an alternating iteration EQU x.sub.n+1 =P.sub.2 (P.sub.1 (x.sub.n))
using the assistance of two projections P.sub.1 and P.sub.2 onto two convex sub-sets of signal spaces, whereby the one sub-set covers those analog input signals of the modulator that generate the binary data stream to be decoded as output signal, and whereby the other sub-set is equal to the space of all band-limited signals that, for example, is spanned by a set of band-limited base signals. The alternating iteration converges toward a fixed point that belongs to the intersection set of the two convex sub-sets. This fixed point signal, consequently, is the sought digital correspondent of that band-limited, analog input signal of the modulator that generates the binary data stream to be decoded as output signal.
The non-linear method described in the Hein and Zakhor reference is thus fundamentally superior to the conventional, linear approach because it employs not only the spectral properties of the input signal for decoding but additionally makes use of the relationship between the input signal and the output signal established by the architecture of the modulator. Unfortunately, this method involves a disproportionally high calculating outlay and is thereby too expensive and too slow, as a result whereof the practical employment thereof is highly limited for decoding sigma delta modulators that can be realized with an especially simple and, therefore, cost-beneficial circuits.